@incollection{AST_2003__284__245_0, author = {Morimoto, Yoshinori and Xu, Chao-Jiang}, title = {Logarithmic {Sobolev} inequality and semi-linear {Dirichlet} problems for infinitely degenerate elliptic operators}, booktitle = {Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony}, editor = {Lebeau Gilles}, series = {Ast\'erisque}, pages = {245--264}, publisher = {Soci\'et\'e math\'ematique de France}, number = {284}, year = {2003}, mrnumber = {2003422}, zbl = {1096.35048}, language = {en}, url = {http://archive.numdam.org/item/AST_2003__284__245_0/} }
TY - CHAP AU - Morimoto, Yoshinori AU - Xu, Chao-Jiang TI - Logarithmic Sobolev inequality and semi-linear Dirichlet problems for infinitely degenerate elliptic operators BT - Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony AU - Collectif ED - Lebeau Gilles T3 - Astérisque PY - 2003 SP - 245 EP - 264 IS - 284 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2003__284__245_0/ LA - en ID - AST_2003__284__245_0 ER -
%0 Book Section %A Morimoto, Yoshinori %A Xu, Chao-Jiang %T Logarithmic Sobolev inequality and semi-linear Dirichlet problems for infinitely degenerate elliptic operators %B Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony %A Collectif %E Lebeau Gilles %S Astérisque %D 2003 %P 245-264 %N 284 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2003__284__245_0/ %G en %F AST_2003__284__245_0
Morimoto, Yoshinori; Xu, Chao-Jiang. Logarithmic Sobolev inequality and semi-linear Dirichlet problems for infinitely degenerate elliptic operators, in Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony, Astérisque, no. 284 (2003), pp. 245-264. http://archive.numdam.org/item/AST_2003__284__245_0/
[1] Wick calculus and the Cauchy problem for some dispersive equations, to appear in Osaka J. Math., 39-1 (2002). | MR | Zbl
and ,[2] Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées, Ann. Inst. Fourier, 19 (1969), 227-304. | EuDML | Numdam | MR | Zbl
,[3] Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477. | DOI | MR | Zbl
and ,[4] Inclusions de Sobolev en calcul de Weyl-Hörmander et systèmes sous-elliptiques, Annales de l'École Normale Supérieure, 30 (1997), 719-751. | DOI | EuDML | Numdam | MR | Zbl
and ,[5] Hypoellipticity in the infinitely degenerate regime, to appear in proceedings of Ohio State university conference on several complex variable. | MR | Zbl
,[6] Un problème aux limites pour une classe d'opérateurs du second ordre hypoelliptiques, Annales de l'Institut Fourier 21 (1971), 99-148. | DOI | EuDML | Numdam | MR | Zbl
,[7] Sobolev and isoperimetric inequalities for degenerate metrics, Mathematische Annalen, 300 (1994), 557-571. | DOI | EuDML | MR | Zbl
, and ,[8] Elliptic partial differential equations of second order, 2nd ed.; Springer-Verlag, Berlin-Now York, 1983. | MR | Zbl
and ,[9] The Dirichlet problem for the Kohn-Laplacian on the Heisenberg group, Parts I and II, J. Funct. Analysis, 43 (1981), 97-142. | DOI | MR | Zbl
,[10] A note on hypoellipticity for degenerate elliptic operators, Publ. RIMS Kyoto Univ., 27 (1991), 995-1000. | DOI | MR | Zbl
,[11] Pseudo-differential operators and non-elliptic problem, Pseudo-Diff. Operators (C.I.M.E., Stresa, 1968), Edizioni Cremonese, Rome (1969), 157-165. | MR
,[12] Hypoellipticity at points of infinite type, Analysis, geometry, number theory: the mathematics of Leon Ehrenpreis (Philadelphia, 1998), Contemp. Math., 251 (2000), 393-398. | MR | Zbl
,[13] The Wick calculus of pseudo-differential operators and energy estimates, "New trends in microlocal analysis" (J.-M. Bony and M. Morimoto, eds.), Springer- Verlag, Berlin, Heiderberg, New York, Tokyo (1996), 23-37. | MR | Zbl
,[14] The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators, Bull. Sc. Math. 121 (1997), 507-547. | MR | Zbl
and ,[15] Hypoellipticity for elliptic operators with infinite degeneracy, "Partial Differential Equations and Their Applications" (Chen Hua and L. Rodino, eds.), World Sci. Publishing, River Edge, NJ, (1999), 240-259. | MR | Zbl
and ,[16] Second order equations with non-negative characterisitic form, Plenum Press, New York London, 1973. | MR
and ,[17] Lower bounds for eigenvalues of regular Strum-Liouville operators and the logarithmic Sobolev inequality, Duke Math. J., 45 (1978), 351-362. | DOI | MR | Zbl
,[18] A weighted inequality and eigenvalue estimates for Schrödinger operators, Indiana Univ. Math. J., 35 (1986), 1-28. | DOI | MR | Zbl
,[19] Note on the class log , Studia, Math. 32 (1969), 305-310. | DOI | EuDML | MR | Zbl
,[20] Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Sc. Norm. Sup. Pisa, 22 (1968), 265-274. | EuDML | Numdam | MR | Zbl
,[21] Microhypoellipticity for a class of pseudo-differential operators with double characteristics, Funkciaj Ekvacioj, 36 (1993), 519-556. | MR | Zbl
and ,[22] Subelliptic variational problems, Bull. Soc. Math. France 118 (1990), 147-169. | DOI | EuDML | Numdam | MR | Zbl
,[23] Regularity problem for quasi-linear second order subelliptic equations, Comm. Pure Appl. Math., 45 (1992), 77-96. | DOI | MR | Zbl
,[24] Semilinear subelliptic equations and Sobolev inequality for vector fields satisfying Hörmander's condition, Chinese J. Contemp. Math., 15 (1994), 183-193. | MR | Zbl
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